We're dividing fractions, so we will flip the one in the denominator upside down and we will multiply it with the numerator.
Let's equal this too 8/x
Cross multiply.
Divide both sides by 15.
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
By using the Distributive Property, you would multiply 3 into the parenthesis (3 · x and 3 · -4)
3(x - 4) = 24
3x - 12 = 24
Then, you would solve like any normal one-step equation.
3x - 12 = 24
+12 +12
__________
3x 36
__ = __
3 3
x = 12, which is your final solution.
If you need any further explanations, please ask me :)
Answer:
-0.875
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
8-10 = -2
-2^2 = -4
